BALANCING CHEMICAL EQUATIONS USING GAUSS-JORDAN ELIMINATION AIDED BY MATRIX CALCULATOR
DOI:
https://doi.org/10.70954/itmj.v2i1.79Keywords:
Balancing equation, Linear Algebra, Gauss-Jordan elimination, Row Echelon Form, Matrix CalculatorAbstract
Balancing equations is among the most complex topics in Chemistry. Teachers find it difficult to teach while the students find it challenging to understand. The way it was taught in Chemistry class is the trial and error approach, which could be tedious and complicated for the students. However, balancing equations could be done easily through the integration of Linear Algebra. This study was anchored on Bruner's Constructivist Theory with emphasis on the heuristic nature of learning using Concrete, Pictorial, and Abstract (CPA) approach. The study utilized the expository research design, which primarily aimed to determine the effectiveness of using Matrix Calculator in balancing chemical equations. In this study, the chemical equation was converted into a system of linear equations and to matrix form. The Matrix Calculator was used to facilitate easy computation. The findings showed that the Matrix Calculator could be an effective teaching tool for Chemistry teachers and could perform complex chemical reactions.
References
Akinola, R. O., Kutchin, S.Y., Nyam, I. A. & Adeyanju, O. (2016). Using row reduced echelon form in balancing a chemical equation. Advances in Linear Algebra and Matrix Theory, 6, 146 – 157. DOI: 10.4236/alamt.2016.64014.
Aplaon, Z.C. & Izon, M. (2015). The teaching practices in Mathematics IV, students’ competence and mastery level in Bongabong Districts. Paper presented in the 2nd International Research Presentation and Seminar, Puerto Galera, Oriental Mindoro, Philippines. MinSCAT, TUCST, and EDS Business School International Research Journal, 2(2), 18 – 24.
Aydin, S. (2009). The factors affecting teaching linear algebra. Procedia Social and Behavioral Sciences 1(2009), 1549 – 1553.
Charnock, N. (2016). Teaching methods for balancing chemical equations: An inspection versus an algebraic approach. American Journal of Educational Research, 4(7), 507 – 511. DOI: 10.12691/education-4-7-2.
Clugston, M., Flemming, R. (2002). Advanced Chemistry. ENG: Oxford University Press.
Croeau, J., Fox, W., & Varazo, K. (2007). Mathematical modeling of chemical stoichiometry. Problems and Issues in Mathematics Undergraduate Studies, 17, 301 – 315.
Dabrowski, A.M., Mitkowski, S. A., Porebska, A. & Kurgan, E. (2010). Formulating structural matrices of equations of electrical circuits containing dependent sources, with the use of the Maple program. Proceedings of 1st World Conference on Technology, Krakow, Poland, September 14 – 17, 2010.
Dalaklioglu, S. Demirci, N., & Şekercioğlu, A. (2015). Eleventh-grade students’ difficulties and misconceptions about energy and momentum concepts. International Journal of New Trends in Education and their Applications, 6, 13 – 21.
Dikovic, L. (2007). Interactive learning and teaching of linear algebra by web technologies: Some examples. The Teaching of Mathematics, X(2), 109 – 116.
Gabriel, C. I., & Onwuka, G. I. (2015). Balancing of chemical equations using matrix algebra. Journal of Natural Sciences, 5(5), 29 – 36.
Gafoor, K. A. & Shilna, V. (2013). Perceived difficulty of chemistry units in Std IX for students in Kerala stream Calls for further innovations. Paper presented at Innovations in pedagogy and curriculum: From theory to practice at GCTE Thalassery, Kerala, April 10 & 11, 2013. Retrieved from https://files.eric.ed.gov/fulltext/ED545397.pdf
Gilat, A., & Subramaniam, V. (2010). Numerical Methods for Engineers and Scientists, 2nd ed., John Wiley.
Idris, I.M. (2003). Toward a right way to teach linear algebra. Mathematics Department, Faculty of Science, Ain-Shans University, Cairo, Egypt. Retrieved from http://www.cimt.org.uk/journal/idris.pdf
Helmenstine, A.M. (2010). Balancing chemical equation. Retrieved from http://chemistry.about.com/cs/stoichiometry/a/aa042903a.htm
Hill, J.W., Mecreary, T.W., & Kolb, D.K. (2000). Chemistry for Changing Times. Pearson Education Inc., 123 – 143.
Hiremath, S. (2013). Balancing chemical equations by using a mathematical model. Retrieved from https://www.researchgate.net/publication/288825280
Hutchings, L., Peterson, L., & Almasude, A. (2007). The Journal of Mathematics and Science. Collaborative Explorations, 9, 119 – 133.
Krishna, Y.H., Ramana Reddy, V. & Praveen, J. P. (2017). Balancing chemical equations using matrix algebra. Journal of Pharmacy and Pharmaceutical Sciences, 6(2), 994 – 999. DOI: 10.20959/wjpps20172_8569.
Lay, D.C. (2006). Linear Algebra and its Applications. Greg Tobin, 17 – 120.
Magbanua, M. & Aplaon, Z.C. (2017). Sex-role in mathematical dichotomy among grade 7 students in Bongabong South. Proceedings in 2017 CEBU International Conference in Business, Management, Education and Law (SBMEL-17), Jan. 26-27, 2017, Cebu, Philippines. Retrieved from http://fze.uconferencealerts.com/siteadmin/upload/DIR0117526.pdf
Malibiran, H., Candelario-Aplaon, Z. & Izon M. (2019). Determinants of problem-solving performance in Mathematics 7: A regression model. International Forum Journal, 22(1), 65 – 86. Available at https://journals.aiias.edu/iforum/article/view/431
McLeod, S. (2019). Bruner’s Constructivism Theory. Retrieved from https://www.simplypsychology.org/bruner.html
Moyo, C. (2018). Investigating the areas of student difficulty in Chemistry curriculum: A case study in Qatar. Texila International Journal of Academic Research, 5(2), 1 – 8. DOI: 10.21522/TIJAR.2014.05.02.Art003
Muehlhauser, L. (2014). 2013 in review: Strategic and expository research. Machine Intelligence Research Institute. Retrieved from https://intelligence.org/2014/02/08/2013-in-review-strategic-and-expository-research/
Myers, R.T., Oldham, K.B., & Tocci, S. (2006). Modern Chemistry: Student Edition. FL: Holt, Rinehart, and Winston.
Padmaja, Y., Harikrishna, Y. & Ramana Reddy, G. V. (2017). An innovative approach of matrix algebra to balancing chemical-reaction equations. World of Journal of Pharmacy and Pharmaceutical Sciences, 6(3), 260 – 266. DOI: 10.20959/wjpps20173_8656.
Özmen, H., & Ayas, A. (2003). Students’ difficulties in understanding of the conservation of matter in open and closed-system chemical reactions. Chemistry Education: Research and Practice, 4(3), 279 – 290.
Risteski, I.B. (2009). A new singular matrix method for balancing chemical equations and their stability. Journal of the Chinese Chemical Society, 56, 65 – 79.
Risteski, I.B. (2010). A new complex vector method for balancing chemical equations. Materials & Technology, 44, 193 – 203.
Risteski, I.B. (2012). New very hard problems of balancing chemical reactions. Chemistry: Bulgarian Journal of Science Education, 21(4), 574 – 580.
Roa, C.N.R. (2007). University General Chemistry: An Introduction to Chemistry Science. Rajiv Beri for Macmillian India Ltd., 17 – 41.
Schmidt, H., & Jignéus, C. (2003). Students’ strategies in solving algorithmic stoichiometry problems. Chemistry Education: Research and Practice, 4(9), 305 – 317.
Stewart, S. & Thomas, M. (2003). Difficulties in the acquisition of linear algebra concepts. New Zealand Journal of Mathematics, 32, S.I. 207 – 215.
Tuckerman, M.E. (2011). Retrieved from http://www.nyu.edu/classes/tuckerman/adv.chem/lectures/lecture_2/node3.html
Vishwambharrao, K.R., Raju, I.N., & Shivarudrappa, H.S. (2013). Balancing chemical equation using mathematical model. International Journal of Mathematical Research & Science, 1(4), 129 – 132.
Wang, Y. (2012). In search of denotational mathematics: Novel mathematical means for contemporary intelligence, brain, and knowledge sciences. Journal of Advanced Mathematics and Applications, 1(1), 4 – 25.
Yuksel, M (2012). Evaluating the effectiveness of the Chemistry education by using the analytic hierarchy process. International Education Studies, 50(5), 79 – 91.
Zabadi, A., & Assaf, R. (2017). From Chemistry to Linear Algebra: Balancing a chemical reaction equation using the algebraic approach. International Journal of Advanced Biotechnology and Research, 8(1), 24 – 33.
Aplaon, Z.C. & Izon, M. (2015). The teaching practices in Mathematics IV, students’ competence and mastery level in Bongabong Districts. Paper presented in the 2nd International Research Presentation and Seminar, Puerto Galera, Oriental Mindoro, Philippines. MinSCAT, TUCST, and EDS Business School International Research Journal, 2(2), 18 – 24.
Aydin, S. (2009). The factors affecting teaching linear algebra. Procedia Social and Behavioral Sciences 1(2009), 1549 – 1553.
Charnock, N. (2016). Teaching methods for balancing chemical equations: An inspection versus an algebraic approach. American Journal of Educational Research, 4(7), 507 – 511. DOI: 10.12691/education-4-7-2.
Clugston, M., Flemming, R. (2002). Advanced Chemistry. ENG: Oxford University Press.
Croeau, J., Fox, W., & Varazo, K. (2007). Mathematical modeling of chemical stoichiometry. Problems and Issues in Mathematics Undergraduate Studies, 17, 301 – 315.
Dabrowski, A.M., Mitkowski, S. A., Porebska, A. & Kurgan, E. (2010). Formulating structural matrices of equations of electrical circuits containing dependent sources, with the use of the Maple program. Proceedings of 1st World Conference on Technology, Krakow, Poland, September 14 – 17, 2010.
Dalaklioglu, S. Demirci, N., & Şekercioğlu, A. (2015). Eleventh-grade students’ difficulties and misconceptions about energy and momentum concepts. International Journal of New Trends in Education and their Applications, 6, 13 – 21.
Dikovic, L. (2007). Interactive learning and teaching of linear algebra by web technologies: Some examples. The Teaching of Mathematics, X(2), 109 – 116.
Gabriel, C. I., & Onwuka, G. I. (2015). Balancing of chemical equations using matrix algebra. Journal of Natural Sciences, 5(5), 29 – 36.
Gafoor, K. A. & Shilna, V. (2013). Perceived difficulty of chemistry units in Std IX for students in Kerala stream Calls for further innovations. Paper presented at Innovations in pedagogy and curriculum: From theory to practice at GCTE Thalassery, Kerala, April 10 & 11, 2013. Retrieved from https://files.eric.ed.gov/fulltext/ED545397.pdf
Gilat, A., & Subramaniam, V. (2010). Numerical Methods for Engineers and Scientists, 2nd ed., John Wiley.
Idris, I.M. (2003). Toward a right way to teach linear algebra. Mathematics Department, Faculty of Science, Ain-Shans University, Cairo, Egypt. Retrieved from http://www.cimt.org.uk/journal/idris.pdf
Helmenstine, A.M. (2010). Balancing chemical equation. Retrieved from http://chemistry.about.com/cs/stoichiometry/a/aa042903a.htm
Hill, J.W., Mecreary, T.W., & Kolb, D.K. (2000). Chemistry for Changing Times. Pearson Education Inc., 123 – 143.
Hiremath, S. (2013). Balancing chemical equations by using a mathematical model. Retrieved from https://www.researchgate.net/publication/288825280
Hutchings, L., Peterson, L., & Almasude, A. (2007). The Journal of Mathematics and Science. Collaborative Explorations, 9, 119 – 133.
Krishna, Y.H., Ramana Reddy, V. & Praveen, J. P. (2017). Balancing chemical equations using matrix algebra. Journal of Pharmacy and Pharmaceutical Sciences, 6(2), 994 – 999. DOI: 10.20959/wjpps20172_8569.
Lay, D.C. (2006). Linear Algebra and its Applications. Greg Tobin, 17 – 120.
Magbanua, M. & Aplaon, Z.C. (2017). Sex-role in mathematical dichotomy among grade 7 students in Bongabong South. Proceedings in 2017 CEBU International Conference in Business, Management, Education and Law (SBMEL-17), Jan. 26-27, 2017, Cebu, Philippines. Retrieved from http://fze.uconferencealerts.com/siteadmin/upload/DIR0117526.pdf
Malibiran, H., Candelario-Aplaon, Z. & Izon M. (2019). Determinants of problem-solving performance in Mathematics 7: A regression model. International Forum Journal, 22(1), 65 – 86. Available at https://journals.aiias.edu/iforum/article/view/431
McLeod, S. (2019). Bruner’s Constructivism Theory. Retrieved from https://www.simplypsychology.org/bruner.html
Moyo, C. (2018). Investigating the areas of student difficulty in Chemistry curriculum: A case study in Qatar. Texila International Journal of Academic Research, 5(2), 1 – 8. DOI: 10.21522/TIJAR.2014.05.02.Art003
Muehlhauser, L. (2014). 2013 in review: Strategic and expository research. Machine Intelligence Research Institute. Retrieved from https://intelligence.org/2014/02/08/2013-in-review-strategic-and-expository-research/
Myers, R.T., Oldham, K.B., & Tocci, S. (2006). Modern Chemistry: Student Edition. FL: Holt, Rinehart, and Winston.
Padmaja, Y., Harikrishna, Y. & Ramana Reddy, G. V. (2017). An innovative approach of matrix algebra to balancing chemical-reaction equations. World of Journal of Pharmacy and Pharmaceutical Sciences, 6(3), 260 – 266. DOI: 10.20959/wjpps20173_8656.
Özmen, H., & Ayas, A. (2003). Students’ difficulties in understanding of the conservation of matter in open and closed-system chemical reactions. Chemistry Education: Research and Practice, 4(3), 279 – 290.
Risteski, I.B. (2009). A new singular matrix method for balancing chemical equations and their stability. Journal of the Chinese Chemical Society, 56, 65 – 79.
Risteski, I.B. (2010). A new complex vector method for balancing chemical equations. Materials & Technology, 44, 193 – 203.
Risteski, I.B. (2012). New very hard problems of balancing chemical reactions. Chemistry: Bulgarian Journal of Science Education, 21(4), 574 – 580.
Roa, C.N.R. (2007). University General Chemistry: An Introduction to Chemistry Science. Rajiv Beri for Macmillian India Ltd., 17 – 41.
Schmidt, H., & Jignéus, C. (2003). Students’ strategies in solving algorithmic stoichiometry problems. Chemistry Education: Research and Practice, 4(9), 305 – 317.
Stewart, S. & Thomas, M. (2003). Difficulties in the acquisition of linear algebra concepts. New Zealand Journal of Mathematics, 32, S.I. 207 – 215.
Tuckerman, M.E. (2011). Retrieved from http://www.nyu.edu/classes/tuckerman/adv.chem/lectures/lecture_2/node3.html
Vishwambharrao, K.R., Raju, I.N., & Shivarudrappa, H.S. (2013). Balancing chemical equation using mathematical model. International Journal of Mathematical Research & Science, 1(4), 129 – 132.
Wang, Y. (2012). In search of denotational mathematics: Novel mathematical means for contemporary intelligence, brain, and knowledge sciences. Journal of Advanced Mathematics and Applications, 1(1), 4 – 25.
Yuksel, M (2012). Evaluating the effectiveness of the Chemistry education by using the analytic hierarchy process. International Education Studies, 50(5), 79 – 91.
Zabadi, A., & Assaf, R. (2017). From Chemistry to Linear Algebra: Balancing a chemical reaction equation using the algebraic approach. International Journal of Advanced Biotechnology and Research, 8(1), 24 – 33.
Downloads
Published
2020-03-09
How to Cite
Candelario-Aplaon, Z. . (2020). BALANCING CHEMICAL EQUATIONS USING GAUSS-JORDAN ELIMINATION AIDED BY MATRIX CALCULATOR. Innovative Technology and Management Journal, 2(1). https://doi.org/10.70954/itmj.v2i1.79
Issue
Section
Articles
License
The copyright holder is the Innovative Technology and Management Journal, Eastern Visayas State University, Tacloban City, Philippines.
